Type-Ambiguous Names Anders J. Schoubye 1

Type-Ambiguous Names Anders J. Schoubye 1 The orthodox view of proper names, Millianism, provides a very simple and elegant explanation of the semantic contribution (and semantic properties) of referential uses of names, namely names that occur as bare singulars and as the argument of a predicate. However, one problem for Millianism is that it cannot explain the semantic contribution of predicative uses of names (as in e.g. there are two Alberts in my class ). In recent years, an alternative view, socalled The Predicativism, has become increasingly popular. According to The Predicativists, names are uniformly count nouns. This straightforwardly explains why names can be used predicatively, but is prima facie less congenial to an analysis of referential uses. To address this issue, The Predicativists argue that referential names are in fact complex determiner phrases consisting of a covert definite determiner and a count noun and so, a referential name is a (covert) definite description. In this paper, I will argue that despite the appearance of increased theoretical complexity, the view that names are ambiguous between predicative and referential types is in fact superior to the unitary The Predicativist view. However, I will also argue that to see why this (type) ambiguity view is better, we need to give up the standard Millian analysis. Consequently, I will first propose an alternative analysis of referential names that (a) retains the virtues of Millianism, but (b) provides an important explanatory connection to the predicative uses. Once this analysis of names is adopted, the explanation for why names are systematically ambiguous between referential and predicative types is both simple and elegant. Second, I will argue that The Predicativism has the appearance of being simpler than an ambiguity view, but is in fact unable to account for certain key properties of referential names without making ad hoc stipulations. 1 Introduction: Referential and Predicative Names Today, the orthodox semantic analysis of proper names is Millianism, the core thesis of which is that a proper name is a singular term whose semantic contribution to propositional content is simply its referent. 2 So, if a name N occurs in a sentence S, the semantic contribution of N to the proposition expressed by S is just the referent of N. In addition to this core thesis, contemporary Millians generally endorse the related theses listed in T2 T5 below. 3 Millianism, as I will use the term here, refers to the conjunction of T1 T5. 1 Draft: 17. April, 2015 2 Cf. Kripke (1979, 1980), Kaplan (1989b,a), Salmon (1986, 1990), and Soames (1987, 2002). 3 I should note that T2 and T3 are consequences of T1. That is, once one accepts the thesis that the meaning of a name is exhausted by its referent, it then follows that the name is rigid and directly referential. These are however importantly different properties and I thus list them separately. The term Millianism was first, I believe, introduced by Kripke (1979, 1) and it is meant to to pay tribute to Mill (1843).

2 ANDERS J. SCHOUBYE T1 Core Millianism A proper name is a singular term, semantic type e, and its semantic contribution to propositional content is simply its referent. T2 Direct Reference The relation between name and referent is direct, that is, the reference of a name is not mediated by any propositional constituent. T3 Rigidity The reference of a name is modally stable, that is the name refers to the same individual in every possible world. For example, the name Gödel refers to Gödel even in counterfactual scenarios where Gödel is not called Gödel or where Gödel is not a famous logician. 4 T4 Fixity The semantic value of a name cannot be affected by logical operators such as modal or temporal operators. Hence, if a name occurs within the scope of a modal, the modal cannot shift the reference of the name. In short, the semantic value of a name is fixed. 5 T5 Ambiguity An expression such as Paul can be to used refer to different individuals on different occasions. The reason is, however, not that Paul is a contextsensitive expression, but rather that this phonological string is lexically ambiguous. For each individual called Paul, there is thus a corresponding (and distinct) lexical entry. Each of these lexical entries are simply morphologically identical homonyms. 6 Millianism provides a straightforward explanation of the semantic contribution of bare singular names in argument position of a predicate, i.e. names as they occur in sentences such as (1) (3). (1) Paul is a linguist. (2) Paul must read Montague. 4 Two kinds of rigidity are occasionally distinguished, namely persistent and obstinate rigidity, cf. Salmon (1981, 32-41). A name is obstinately rigid if it refers to the same individual in all possible worlds, even worlds where that individual does not exist. By contrast, a name is persistently rigid if it refers to the same individual in all worlds where the individual exists (and fails to refer in worlds where that individual does not exist). Nothing in my discussion hangs on the choice between these notions, so I remain neutral on this issue here. 5 I refer to this kind of immunity to shifting as Fixity following Schlenker (2003, 29). 6 For arguments in favor of the lexical ambiguity view, cf. Kripke (1980, 7-9), Kaplan (1989b, 558-563), Kaplan (1990), and Soames (2002, 96-103).

Type-Ambiguous Names 3 (3) If Paul sent Paul a book last year, Alfred should have received it by now. It seems intuitively correct that the semantic contributions of the names in (1) (3) are simply the referents, and moreover that the names are directly referential, rigid, and fixed. For ease of exposition, I will refer to bare singular uses of proper names in argument position of a predicate as referential uses, or sometimes simply as referential names. 7 However, like common count nouns, proper names can combine syntactically with a wide range of determiners, e.g. definite and indefinite determiners, numerical determiners, demonstratives, and wh-phrases. These uses of names, namely uses where the name occurs as the syntactic sister of a determiner, are standardly referred to as predicative uses (I will sometimes simply use the term predicative name for these occurrences). 8 For example, consider (4) (12). (4) There are relatively few Alfreds in Princeton. (Burge, 1973, 429) (5) A Smith is in the kitchen. Another is in the garden. (6) Three Alfreds asked questions during the lecture. (Hawthorne and Manley, 2012, 219) (7) The Alfred who joined the club today was a baboon. (Burge, 1973, 429) (8) Every Sarah I ve met sometimes works as a babysitter. (Fara, 2015b, 61) (9) Most Alfreds are crazy. (Elbourne, 2005, 171) (10) Do you mean this Alfred? (Elbourne, 2005, 171) (11) Which Alfred do you mean? (Elbourne, 2005, 171) (12) Sarahs from Alaska are usually scary. (Fara, 2015b, 61) One problem for Millianism is that there is no straightforward way of reconciling the intuitive truth conditions of the sentences in (4) (12) with the assumptions in T1 T5. In other words, predicative uses of names are not, it would seem, consistent with an analysis of names as directly referential, rigid, and fixed singular terms. 1.1 Predicativism One alternative to Millianism is Predicativism. This is the view that proper names are uniformly predicative, i.e. the contribution of a name to propositional content is a predicate. So, the meaning of the name Paul might be the property of being called 7 This is merely terminological convenience, and hence not meant to prejudge either semantic function or semantic properties of these names. 8 I mean to include cases here where a name is part of a larger syntactic constituent which is the sister of a determiner, cf. e.g. (7) and (8) below. Proper names also have bare plural uses, cf. (12).

4 ANDERS J. SCHOUBYE Paul, the property of bearing the name Paul, or some such variant. Moreover, when a name is used referentially, the name is typically analysed as shorthand for some complex determiner phrase, e.g. The person called Paul (e.g. Kneale, 1960), That Paul (e.g. Burge, 1973), The thing which is the bearer of Paul (e.g. Katz, 2001), The Paul (e.g. Sloat, 1969). 9 One Predicativist view that seems to be gaining popularity is The Predicativism. 10 Proponents of this view, namely Elbourne (2005), Matushansky (2006, 2008), and Fara (2011, 2015a,b) argue that names are count nouns. So, just as the count noun tiger denotes a property, a name such as Paul also denotes a property, namely the property loosely characterised by the function λx: x D e. x is called Paul. 11 This analysis of names makes it straightforward to explain predicative uses, i.e. why names can occur as the syntactic arguments of quantificational determiners, cf. the sentences in (4) (12), and it also makes it easy to explain why names have bare plural, i.e. generic, uses. In addition, proponents of The Predicativism provide several other convincing semantic and syntactic arguments for the claim that names should be analysed as predicates. To give just one example, Matushansky and Fara provide ample evidence that contrary to immediate appearances, the verb call is not ditransitive (i.e. does not have three argument places) in constructions such as (13) below. (13) My parents called me Delia. (Fara, 2015b, 67) Instead it is a transitive verb whose direct object is a so-called small clause, viz. the clause me Delia in (13). Within this small clause, me is in subject position and Delia is in what is syntactically predicate position. In other words, the name Delia is a predicate in (13), cf. Matushansky (2005) and Fara (2011, 2015b) for details. What sets The Predicativism apart from other Predicativist views is that proponents of The Predicativism maintain that when a proper name occurs in argument position of a predicate and as a bare singular, cf. (1) (3) above, the proper name is in fact the syntactic argument of a covert and phonologically null, i.e. unpronounced, definite determiner. In other words, the logical form (LF) of a sentence such as (1) is roughly (14), cf. Fara (2015b, 70-71). 9 Predicativism is sometimes distinguished from so-called Metalinguistic Descriptivism, but I use the term here as a general term for a family of related views. Early proponents of Predicativism include Quine (1960), Kneale (1960), Sloat (1969), and Burge (1973), but in the last two decades, it has been defended in various forms by several other people including Hornsby (1976), Bach (1981, 1987, 2002), Geurts (1997), Katz (2001), Elbourne (2005), Matushansky (2006, 2008), Sawyer (2010), Fara (2011, 2015a,b), and Gray (2014). See also Larson and Segal (1995). 10 Since there are important differences between Elbourne s, Matushansky s, and Fara s views, the following characterisation of The Predicativism leaves out a number of details. However, when details are relevant, I will include these. 11 I use the notation standard from Heim and Kratzer (1998). In an expression of the form λα: N. M, α is an argument variable, N is a domain condition indicating the domain of the function and M is a value description.

Type-Ambiguous Names 5 (1) Paul is a linguist. (14) [ S [ DP the Paul] [ VP is a linguist]] S: t DP VP: et D NP: et is a linguist the N In a standard extensional semantics (and assuming a Fregean referential analysis of definite descriptions), the truth conditions of (1) are thus to be derived as follows: the proper name Paul in (1) is a predicate that combines compositionally with the covert definite determiner to form a referential expression of semantic type e. This referential expression then combines with the VP to form an expression of type t. 12 This demonstrates one of the primary selling points of The Predicativism and perhaps its most significant advantage over Millianism, namely that it provides a uniform and compositional analysis of names that can provide an explanation for both predicative and referential uses. 13 Paul 1.2 Type Ambiguity Faced with the problem of predicative uses, it might seem that there is an obvious and simple solution to this problem that proponents of Millianism could endorse. The Millian could, for example, argue that the phonological string Paul is not only lexically ambiguous (i.e. that there are multiple homonyms of Paul in the lexicon), but moreover that each individual homonym is ambiguous between a directly referential singular term (referring to a specific individual) and a predicate (expressing the property of being called Paul). This would thus amount to the view 12 However, as noted by a referee for this journal, whether to treat the definite article as a function from properties to individuals is independent of the Predicativist thesis that names are predicates. Predicativism is perfectly compatible with an analysis of the as a genuine quantificational determiner, viz. semantic type et, et,t, and an analysis of the as a predicate modifier, viz. semantic type et,et, see Fara (2001). Predicativists such as Elbourne (2005) and Matushansky (2008) both seem to favour a Fregean analysis. 13 Millianism and Predicativism obviously do not exhaust the space of possible views about proper names. There is, for example, a variety of other famous descriptivist view, e.g. Frege s (1892) sense theory, Russell s (1905, 1956) famous deeds descriptivism, Searle s (1958) cluster theory of names, and others. However, since The Predicativism is becoming increasingly popular (and since I take it to be the most empirically adequate of the non-millian views), I restrict my focus to this view here.

6 ANDERS J. SCHOUBYE that names come in two different types, a referential type and a predicative type. While this analysis would entail that names are both lexically ambiguous and type ambiguous, it could also salvage Millianism for the referential uses of names. 14 Henceforth, I will refer to the view that name have two distinct types, namely a referential type and predicative type, as the type-ambiguity view. This view, I should emphasise, is compatible with different analyses of referential and predicative names respectively, it just assumes that names invariantly come in these two types. 15 So someone who endorses Millianism for referential names can simultaneously endorse the type ambiguity theory and this might seem like the simplest and most obvious way for a proponent of Millianism to account for predicative names. The problem is that there are a number of significant explanatory challenges for this view, e.g. (E1) (E3) below. 16 Inferential Patterns (E1) It is natural to think that some important relation holds between the meaning of a referential name and the meaning of its predicative counterpart. In particular, one might think that this relation in meaning is what explains why any normal utterance of e.g. Jones is a Jones (Burge, 1973, 429) seems obviously true or more generally why certain inferences involving referential and predicative names are, at least intuitively, instances of perfectly good reasoning. Consider, for example, the inferences below: Paul is tired So, at least one Paul is tired IF1 No Pauls are tired So, Paul is not tired IF2 While the inferences in IF1 and IF2 are not necessarily truth preserving (and thus not valid in the sense of being true at every world in every model), there is nevertheless something intuitively compelling about these inferences. 17 For instance, they seem 14 This is, roughly, the view defended by Leckie (2013). More specifically, Leckie argues that names are polysemous between referential and predicative uses. 15 Some complain that what I call type-ambiguity is really polysemy. This is mostly a terminological dispute. I use the expression type-ambiguity for two reasons. First, I find that the notion of polysemy is rather inclusive and often extended to phenomena that I consider quite disparate, e.g. so-called deferred reference and predicate transfer, cf. Nunberg (1995). Second, the type of meaning difference that I am arguing is systematically observable with names is more reminiscent of the type of meaning difference observed in and famously referred to as type-ambiguity by Partee and Rooth (1983). Lastly, on the view that I am advocating, the lexicon would contain one entry for a referential name and a distinct entry for the predicate. 16 These challenges are explicated in detail and discussed by Leckie (2013, 1143ff), however the challenge in E1 was, I believe, first observed by Hornsby (1976, 228-229). I use Leckie s terminology for several of these challenges. 17 Since validity is standardly explicated as truth in all worlds of every model, notice that there might be possible worlds where Paul is tired, but where he is not called Paul.

Type-Ambiguous Names 7 to satisfy the following intuitively plausible constraint on good inferences: For any context c, if the premise(s) can be uttered truly in c, the conclusion must be true in c. 18 To illustrate, consider IF1: If a speaker can truly utter Paul is tired in a given context, it intuitively follows that at least one Paul is tired in that context. 19 For proponents of The Predicativism, explaining why IF1 and IF2 satisfy the constraint above is not a problem it follows directly from their analysis of bare singular names in argument position of a predicate. On this analysis, the name Paul in the premise of IF1 combines with a phonologically null definite determiner yielding a definite description of the form the Paul. That description can refer to an individual x only if x is called Paul, and as a result the premise is predicted to be true iff the (unique) individual called Paul is tired. This premise can thus obviously be true in a context only if the conclusion is too. By contrast, if a proponent of Millianism avails herself of the type-ambiguity view to account for the predicative uses, inferences such as IF1 and IF2 constitute a non-trivial challenge. On the Millian view, the content of the name in the premise of IF1 is just its referent, i.e. it is not part of the semantics of the name that its referent must be called Paul. Hence, to explain why e.g. IF1 seems to satisfy the condition above, viz. that whenever its premise can be uttered truly, the conclusion must be true too, the Millian cannot appeal to the semantics of the name. As a consequence, the Millian must maintain that something else explains why IF1 seems intuitively to satisfy this condition. The question, of course, is what exactly this something else is? On the one hand, it cannot be part of the meaning of the name (nor, I presume, part of the meaning of the predicate), so it would have to be something that goes beyond the meaning of the constituents and their truth conditional composition, viz. something non-semantic. On the other hand, it must be something that can constrain when the premise can be uttered truly. However, something that constrains the conditions under which a sentence can be uttered truly seems to constrain the truth conditions more generally. So such a constraint is presumably a semantic constraint (i.e. a constraint on the meaning of the name)? There is, therefore, a genuine challenge for Millians quite generally, namely how to explain that these inferences are intuitively compelling without appealing to any semantic relation between referential and predicative names. 18 While this principle is formulated in terms of utterances, we should distinguish between utterances and saentences-in-a-context. As Kaplan (1989b, 522) notes: [...] it is important to distinguish an utterance from a sentence-in-a-context. The former notion is from the theory of speech acts, the latter from semantics. Utterances take time, and utterances of distinct sentences cannot be simultaneous (i.e., in the same context). But in order to develop a logic of demonstratives we must be able to evaluate several premises and a conclusion all in the same context. (Kaplan, 1989b, 522). Hence, the relevant notion here is really sentences-in-a-context. 19 On the assumption that the determiner phrase No Fs can only be used appropriately when the domain of Fs is non-empty, IF2 would also intuitively satisfy this constraint.

8 ANDERS J. SCHOUBYE Here is an explanation that I suspect a Millian might propose in response: While it is not part of the meaning of Paul, it is a constraint on its use that it can only refer to individuals called Paul. So, it is only possible to truly utter the sentence Paul is tired in a context c if the intended referent is called Paul in c. The problem with this suggestion is that it is difficult not to take this constraint on the use of Paul as part of its meaning (i.e. its semantics). Since, on this explanation, the constraint directly determines what the name can be used to refer to, and so directly impacts the truth conditions of any utterance that contains the name, this looks like a semantic constraint. So, if that explanation is correct, there is something to the meaning of a name over and above its referent and this then is no longer the standard Millian view. Competence (E2) Linguistic competence with referential and predicative names appears to be closely connected. For example, if a speaker understands the meaning of a bare singular name (i.e. a referential name), that speaker would under normal circumstances also understand the meaning of its predicative counterpart. In other words, a speaker who understands (15) is also typically capable of understanding (16). (15) Paul is tired. (16) There is at least one Paul who is tired. Again, an explanation of this competence follows directly from The Predicativism: If names are uniformly predicates, there is then no semantic difference between the names in (15) and (16). In contrast, providing an adequate explanation of this competence is less straightforward if it is assumed that the meaning of the name in (15) is exhausted by its referent. Indeed, it seems natural to assume that any adequate explanation of the observation about competence must rely on the meaning, i.e. the semantics, of the names, but such an explanation is not immediately available to the Millian who also endorses the view that names are ambiguous between referential and predicative meanings. Hence, with regards to competence, it also seems that there is a prima facie challenge for this view. Intra and Cross-Linguistic Uniformity (E3) Finally, if names are ambiguous between predicative and non-predicative kinds, this would mean that certain languages have a rather staggering number of ambiguities. For example, in English, it seems that all names have both predicative and referential uses (Intra-linguistic Uniformity). In addition, both referential and predicative uses of names are attested in a variety of other languages (Cross-linguistic Uniformity). The question for a proponent of the type-ambiguity view is what explains this kind of uniformity both language internally and across languages. If names are genuinely type-ambiguous, would it then just have to be a massive coincidence that

Type-Ambiguous Names 9 this ambiguity is cross-linguistically ubiquitous? That seems very implausible. In contrast, it seems that proponents of The Predicativism completely avoid the need to address these potential problems as names are simply not ambiguous according to their view. Conclusion In conclusion, the type-ambiguity view (with referential names construed as Millian names) faces some non-trivial challenges and it is unclear how to adequately resolve these challenges while maintaining T1-T5 above for referential names. So, this does not look like an easy way out. On the other hand, sticking to the assumption that all occurrences of names are invariantly Millian just leaves it entirely mysterious how to explain the widely attested predicative uses. In contrast, The Predicativism provides direct and elegant solutions to these challenges, so one might be tempted to conclude that The Predicativism has the advantage here. 20 However, before proceeding to my proposed analysis, let s first quickly summarise the three positions considered so far. (Strict) Millianism (names as uniformly singular terms) Proper names are uniformly directly referential singular terms, semantic type e, and the meaning of a name is simply its referent. Moreover, proper names are directly referential, rigid, fixed, and lexically ambiguous. Seemingly non- Millian uses of names (e.g. various predicative uses) must either be explained away or, somehow, be explained in terms of the relevant singular terms. Predicativism (names as uniformly predicates) Proper names are uniformly predicative, semantic type e,t, and the meaning of a name N is roughly the property λx: x D e. x is called N. Bare singular uses of names must be explained as derived from, or piggybacking on, the predicational uses. Type-Ambiguity (names as systematically ambiguous) Proper names are type-ambiguous between expressions denoting individuals 20 One response on behalf of the Millian is given by Leckie (2013) who argues that Millians can meet these challenges by appealing to the general phenomena of metonymy. Moreover, Leckie also argues that to explain metonymic relations, both lexical rules and pragmatics are needed and such lexical rules and pragmatics suffice to bridge the putative gap between Millian names and predicative names. Leckie s view is interesting and ultimately, for the purposes of this paper, I am willing to grant that for proponents of Millianism (as characterised by T1 T5 above), Leckie s proposal may be the best option. My proposed view shares some similarities with Leckie s view, but I will argue that there is a simpler and theoretically more elegant way of meeting these challenges that will not require any auxiliary assumptions about metonymic relations or lexical rules and which will have additional explanatory power. That option is to adopt the semantics of referential names that I propose in the following sections.

10 ANDERS J. SCHOUBYE (e.g. singular terms) and expressions denoting properties (e.g. predicates). For example, one might propose to be Millian about referential names but Predicativist about the predicative uses of names. The challenges in E1 E3 arise for proponents of this latter view. 21 1.3 Thesis: A Defense of Type-Ambiguous Names The thesis to be defended in the present paper is the following: Proper names are type-ambiguous more specifically ambiguous between predicates and singular terms. The semantic type of a predicative name is the same as the type of a count noun, viz. type e,t in a simple extensional semantic framework. In contrast, when a name occurs grammatically as a bare singular, it is an individual-denoting singular term and therefore semantic type e. I will henceforth indicate name types using superscripts: Paul P for the predicative type and Paul R for the referential type. Instead of adopting and defending the orthodox Millian analysis for referential names, I will present an alternative that retains the primary virtues of Millianism, but also provides a number of additional advantages. One specific advantage is that referential names and predicative names turn out to share a crucial piece of semantic content. This shared content will suffice to resolve the challenges discussed above. In other words, I will show that there are very strong reasons for favoring the type-ambiguity view. Moreover, my arguments will show that the ambiguity in question is benign, i.e. it does not add gratuitous theoretical complexity. As regards theoretical parsimony, the type-ambiguity view is, at the very least, on a par with The Predicativism. In the second half of the present paper, I will argue that The Predicativism, despite being the most promising Predicativist view, faces significant problems. First, I will demonstrate that proponents of The Predicativism either have no means for providing a principled explanation of the rigidity of proper names. Second, I will demonstrate that the behaviour of definite descriptions in English is inconsistent with the behaviour of names in argument position of a predicate. In other words, the assumption that names are covert descriptions leaves several serious explanatory gaps. These problems show that the uniform analysis offered by The Predicativism comes with considerable costs. So, as far as theoretical parsimony is concerned, the type-ambiguity view is superior. 2 Two Types of Names: Predicates and Pronouns Let s start by considering the syntax and semantics of predicative names. 21 However, proponents of strict Millianism are obviously no better off. On this view there simply is no explanation of predicative uses.

Type-Ambiguous Names 11 PREDICATIVE NAMES Predicative names, let s assume, are just like count nouns: Semantically these names denote properties, i.e. functions from individuals to truth values, and their (extensional) semantic type is therefore e,t. To a rough approximation, the lexical entry for a predicative name, e.g. Paul, is the following: (17) Paul P c,g,w = λx: x D e. x is called Paul in w 22 As mentioned already, when predicative names are analysed as count nouns, this straightforwardly explains why it is possible for names to combine with quantificational determiners as illustrated by examples (4) (12) above. Finally, like other count nouns, e.g. bears in (18), predicative names also have bare plural uses. This explains why names can be used to make generic statements, cf. e.g. (19). (18) Bears from Alaska are dangerous. (19) Sarahs from Alaska are dangerous. In short, I propose to analyze this particular class of names (viz. the predicative names) in the way roughly suggested by proponents of The Predicativism. However, since I think that there are non-trivial problems with The Predicativism, there are good reasons to suppose that referential names are of a different type. REFERENTIAL NAMES Rather than the Millian analysis of names as individual-denoting constants whose meanings are simply the referents, I propose an alternative analysis. I propose that referential names, i.e. names that occur as bare singulars in argument position of a predicate, be analysed as expressions that can refer to different individuals across contexts and whose semantic values are determined by a contextually determined variable assignment rather than a model theoretic interpretation function. On my proposed analysis, a proper name is thus formally a variable rather than an individual-denoting constant. In slogan form, a proper name is a pronoun. 23 22 A more sophisticated formulation of the naming relation is most likely needed, but there is some disagreement even among proponents of The Predicativism on this issue, cf. Matushansky (2008, 592f) for extensive discussion. I use the perhaps naive x is called N in this paper, but nothing in my analysis hangs on this assumption. I simply leave it to proponents of The Predicativism to determine which analysis and formulation of the naming relation is empirically superior. Whichever is deemed superior, I will use that condition both in my analysis of predicative names and in my analysis of referential names, cf. section 2.2 23 There are several important predecessors to the view that I am defending here. First, an early and closely related analysis is Recanati (1993, 135-146), where proper names are analysed as a type of indexical with corresponding descriptive characters. Also, Lasersohn (forthcoming), in a currently unpublished manuscript, has proposed an analysis of names that is very similar to my proposal here. However, neither Recanati nor Lasersohn discuss nor relate their analyses to the problems raised here. Moreover, general proposals to analyse

12 ANDERS J. SCHOUBYE Analysing referential names as pronouns allows one to retain the most desirable features of Millanism but also provides additional advantages including a quite elegant way of bridging the putative gap between referential and predicative names. However, to make clear the intended analysis of proper names envisioned here, we need to start by outlining the semantics of pronouns. 2.1 Pronouns According to the now widely considered standard analysis of pronouns in Heim and Kratzer (1998, 239-260) building on Cooper (1983, 176-194) a pronoun is a numerically indexed expression whose semantic value is a function of a variable assignment g (where g is a function from numbers to individuals in the domain of the relevant model). The variable assignment is generally assumed to be a function of the discourse context and can informally be thought of as a model of the speakers intentions. While variable assignments determine semantic values of pronouns, there are important constraints on such assignments. For example, a pronoun she can have an individual d as its semantic value only if d is female (gender), a single individual (number), and neither the speaker nor the addressee (person). These constraints on assignments correspond to grammatically represented features standardly called φ-features for pronouns in English these are gender, number, and person features. 24 φ-features are often assumed, see e.g. Heim and Kratzer (1998, 244-245) and Heim (2008, 35-37), to be syntactically realised with each φ-feature occupying an individual node in a phrase structure, cf. the phrase structure below. Semantically, these features are treated as partial identity functions f and they are defined only if names as variables have been around for a while, see especially Dever (1998) and more recently Cumming (2008). There are, however, important differences between these proposals and mine most obviously that my proposed analysis includes a crucial constraint on the assignment of semantic values to proper names. Moreover, Cumming, for example, insists (for reasons that are unclear to me) that names are not context-sensitive and I explicitly reject this assumption. Another view that deserves mentioning is Charlow (2013), especially p.516-517. Charlow s analysis assumes that names trigger existence presuppositions that provide information about the relation between name and referent. While Charlow s analysis is not exactly an analysis of names as variables, his analysis does have more resources than standard Millianism, for example resources to deal with e.g. E1 discussed earlier. However, Charlow s analysis also has the consequence that proper names should have straightforward attributive uses which they do not. I discuss this issue in more detail later. It is also sometimes argued that the view that proper names are variables or pronouns is very close in nature to the analysis of names in various versions of dynamic semantics, e.g. Discourse Representation Theory, cf. Kamp and Reyle (1993), Asher (1986), van der Sandt (1992). I think this is a rather subtle issue and it is not something that I wish to discuss here. However, as I am myself an advocate of dynamic semantics, cf. Schoubye (2011, 2013), and since my view is perfectly compatible with various dynamic systems, I am more than happy to include various dynamic semantic approaches as precursors to the view defended here. 24 For an extended discussion of the syntax and semantics of φ-features, see Heim (2008).

Type-Ambiguous Names 13 the individual d, determined by g, is in the domain of f. If d satisfies the relevant domain constraint associated with f, the output of the function is simply d. If not, semantic computation comes to a halt and no proposition is expressed. In short, φ- features represent a type of presuppositional constraint on assignments of semantic values to pronouns, cf. (21) (23). (20) she i c,g,w = g(i) DP (21) 3rd person = λx : x D e and x is neither the speaker nor the addressee in w c. x (22) feminine = λx : x D e and x is female in w c. x [3rd person] [feminine] DP DP (23) singular = λx : x D e and x is singular in w c. x [singular] DP she i From a semantic point of view, these syntactic assumptions about φ-features are not strictly required. For example, one could instead assume the φ-features are not syntactically realised but simply included directly in the semantics of pronouns. For example, consider (24). (24) she i c,w,g = g(i) if g(i) is a single individual in w c g(i) is female in w c g(i) is not speaker nor addressee in w c = undefined otherwise This explication of φ-features can easily be generalised to other pronouns and it yields equivalent semantic results with less syntactic commitments. This analysis of pronouns is very similar to Kaplan s (1989b, 1989a) analysis. In a sense, the Kaplanian notion of character is here captured in terms of φ-features. Kaplanian characters are roughly speaking linguistic rules associated with expressions and these rules are, for Kaplan, determinants of semantic values in context (although not part of the propositional content). For instance, the character of you is something like the addressee in the context of utterance which relative to such a context determines an individual. On the view proposed here, this character would be encoded as a presuppositional constraint on uses of you, i.e. such uses are predicted to be acceptable only if the intended referent, determined by the

14 ANDERS J. SCHOUBYE variable assignment, has the property of being the addressee of the utterance in the context. 25 As in Kaplan s original analysis, this analysis renders pronouns directly referential, rigid, and fixed. Firstly, since the semantic value of a pronoun is determined directly by a variable assignment, its semantic value is not mediated by a propositional constituent (direct reference). Secondly, if a sentence S contains a pronoun α that refers to b relative to context c, then if the proposition expressed by S in c is evaluated relative to different possible worlds, the reference of α is b at every possible world (rigidity). Thirdly, since the assignment function is what determines the semantic value of the name, its reference can only be shifted (i.e. changed) by logical operators that operate on variable assignments. Since modal and temporal operators operate on world and time parameters, names cannot be shifted by such operators (fixity). In conclusion, names are directly referential, rigid, and fixed. 26 Another important feature of this analysis is that it treats pronouns as contextsensitive rather than as lexically ambiguous. Standard examples of lexical ambiguity in English include bat, strike, case, etc. For example, bat can be used to talk about a winged nocturnal animal or a piece of sporting equipment, but these meanings are unrelated and moreover expressed by different words in other languages. It is therefore generally assumed that these meanings are also expressed by different words in English words that as a matter of mere coincidence are homonyms. So, while the string bat, can refer to at least two unrelated types of things, these things are in fact referred to by different words, e.g. bat 1 and bat 2, and these words have different characters. In contrast, that a pronoun such as she can be used to refer to different individuals is not intuitively a good reason to conclude that she is multiply ambiguous, i.e. that the lexicon contains she 1, she 2... she n. Pronouns are sensitive to context in a way that lexically ambiguous words are not. So, when the word she is used to refer to different individuals, even within one context, this is intuitively simply a 25 In other words, φ-features are not exactly like characters. On the Kaplanian view, character plus context determine semantic value whereas φ-features only constrain what semantic value an expression can be assigned given a context. However, for my purposes, this difference between Heim and Kratzer s analysis and Kaplan s analysis is of no concern. 26 Pronouns can, however, be shifted by quantificational determiners. Indeed, if a pronoun is co-indexed with a quantifier, the quantifier is generally assumed to shift the variable assignment to a modified assignment, cf. Heim and Kratzer (1998) for details. This follows from the standard Tarskian semantics for quantifiers, cf. Tarski (1933). However, this in effect means that quantifiers are monsters (in Kaplan s (1989b) terminology) for discussion see e.g. Rabern (2013). To indulge in a bit of Kaplan exegesis, it could be argued that Kaplan could avoid this consequence by sharply distinguishing bound and unbound variables, i.e. by assuming that the variables (pronouns) that are bound are simply different expressions than the variables that are unbound (deictic pronouns). In various places, e.g. Afterthoughts (1989a, 571ff), this appears to be Kaplan s favoured view. Yet, in other places, e.g. Kaplan (1989b, 541ff), bound and unbound variables are treated alike. Hence, it is not entirely clear what Kaplan s view is.

Type-Ambiguous Names 15 case of multiple uses of the same word. A single word means a single character, but because of its variable nature (its context-sensitivity), different uses of this word can be assigned different referents. 27 Another reason to think that there is a difference between the context-sensitivity of pronouns and lexical ambiguity is this: it would be entirely unsurprising and unremarkable if some speaker S was competent with only one meaning of a lexically ambiguous word. For example, S might know that bat is used to talk about a piece of sporting equipment, but not know that it is also used to talk about nocturnal animals. In contrast, it would be surprising and quite remarkable if, say, the word she was part of S s vocabulary (i.e. suppose S used the word to refer to his mother), yet S was unaware that it can be used to refer to different individuals. Indeed, one might think that S, in this case, is just not competent with the meaning of she. In contrast, in the previous case, it does seem that S is competent with one of the meanings of bat. 2.2 Proper Names as Pronouns My proposed analysis of referential proper names is now quite simple. It is simply a variant of the analysis of pronouns above. Specifically, I propose that the lexical entry for the referential variant of a name, e.g. Paul, is the following: (25) Paul s i c,g,w = g(i) if g(i) is called Paul in w c = undefined otherwise According to this analysis, the name Paul is essentially a pronoun. The referent of the name depends on a (contextually determined) variable assignment which we 27 Given that the semantic value of a pronoun is determined by a variable assignment, this analysis requires that pronouns come equipped with indices, i.e. she 1, she 2... she n. Moreover, each of these will need a separate lexical entry. But, if the lexicon contains she 1, she 2... she n, not only are we committed to a potential infinity of variables in the lexicon (an objection often pressed by proponents of so-called variable-free semantics, cf. e.g. Jacobson 1999; 2000; 2014), this also looks technically indistinguishable from ambiguity. Someone might therefore object to my claim that it is an advantage of my view that (spoiler alert) names are context-sensitive (rather than lexically ambiguous) when my analysis essentially treats names as a type of pronoun, i.e. as a numerically indexed variable. This is an important but complex issue, so I will only make a brief comment here. First, notice that the superscripts associated with e.g. bat are merely intended to help distinguish one homonym from another, i.e. these are not semantically interpretable. In contrast, the index associated with a pronoun is semantically interpretable, indeed it is essential to its semantic interpretation. Second, the semantic value of a pronoun is determined by a variable assignment (which in turn is determined by context), whereas the semantic value of, say, bat 1 is determined by the model. I take it that this difference is also meant to generally reflect that the meaning of any given pronoun is sensitive to context in a way that e.g. bat 1 is not. Much more could, and have been, said about this issue, see e.g. Braun (1996), Gauker (2014), Dever et al. (2014).

16 ANDERS J. SCHOUBYE may suppose informally represents speakers intentions. Hence the name can refer to different individuals across different contexts. However, the name is constrained in the sense that it can only refer to individuals who are called Paul. In other words, the variable assignment g only returns an individual d for argument i if d is in the domain of the function in (26). (26) λx : x D e and x called Paul. x This constraint on the assignment of semantic values to names can be thought of as a way of cashing out (at least part of) the character of the name. 28 This analysis retains the most important virtues of Millianism (as defined earlier). First, a name is a singular term that refers directly and without the mediation of any propositional constituent to its (intended) referent, viz. it is directly referential. Second, if a sentence S contains a name N that refers to b relative to context c, then if the proposition expressed by S in c is evaluated relative to different possible worlds, the referent of N is b at everyone of those possible worlds. Hence, names are rigid. Third, since the referent of a proper name is controlled by a contextually determined variable assignment, its reference can only be shifted by operators that operate on variable assignments. Thus, it cannot be shifted by modal or temporal operators, and so names are fixed. This analysis of names does, however, diverge from Millianism in one respect, namely in that it does not analyse names as individual-denoting constants. Remember, on the Millian view, it is assumed that e.g. Paul McCartney and Paul Newman have different first names. While these first names happen to be homonyms, they are nonetheless different: One is the first name of Paul McCartney, the other is the first name of Paul Newman. Personally, I find this a particularly counterintuitive consequence of Millianism and I am therefore more than happy to relinquish the assumption that gives rise to it. 29 It seems much more plausible that proper names are simply context-sensitive expressions expressions that can refer to different individuals on different occasions of use. This is precisely what my proposed view predicts. I.e. according to my view, McCartney and Newman have the same first name, but that name can, on different occasions of use, be used to refer to either of them. In conclusion, the analysis of proper names as pronouns retains the best features of Millianism and moreover provides the advantage of avoiding lexical ambiguity. 28 Again, as mentioned earlier, we may need a more sophisticated naming constraint. I remain agnostic on that question, but cf. footnote 20. 29 For a more extensive discussion of the problems with the assumption that names are lexically ambiguous, see e.g. the discussion in Katz (2001, 150-154)

Type-Ambiguous Names 17 2.3 Meeting the Challenges to the Type-ambiguity View The analysis of names as pronouns also provides a straightforward answer to the challenges discussed in section 1.2. To see this, let s start with Inferential Patterns (E1). Given my proposed analysis, it is very simple to explain why the inferences in IF1 and IF2 (and other related inferences) are intuitively compelling. For example, consider again IF1 below. Paul is tired So, at least one Paul is tired IF1 For the premise Paul is tired to be true, the variable assignment must map the index associated with the name Paul to some individual a in the domain. However, in order for the assignment function to return a (i.e. the individual associated with the index), a must be called Paul this is the semantic constraint associated with the name. So, it follows that for the premise Paul is tired to be true, there must be (at least) one individual x in the context such that x is called Paul and x is tired. But this is, of course, simply the truth condition of the conclusion of IF1. So, when the premise is true at some context c, the conclusion is then also true at c precisely as desired. However, notice that this analysis does not render IF1 necessarily truth preserving (and it should not), because the truth of the premise at some context c is consistent with the possibility of there being possible worlds where the referent determined by g(c) is not called Paul (and, so, where no Pauls are tired). 30 In conclusion, this analysis captures one natural sense in which the inference is correct without predicting that it is necessarily truth preserving. Moreover, the explanation generalises straightforwardly to IF2 and other related inferences. Before proceeding to the challenge in (E2), let me add a remark with respect to Millianism: As noted earlier, it seems that Millians need an alternative explanation of the intuitive acceptability of the inferences in IF1 and IF2. Moreover, it is not 30 Given that the inference is not necessarily truth preserving, it is not valid in the sense of being true at every world of every model. However, as argued by Montague (1968), Kaplan (1989b) and others, a restricted notion of validity is needed in order to assess sentences and arguments containing indexical terms (e.g. pronouns) or what Montague (1968) called pragmatic languages. To this end, Kaplan (1989b) introduces the notion of indexical validity where a sentence φ is defined as indexically valid iff it is true at every context of every model. This definition combined with certain constraints on (the contexts of) of the model, namely that a context must be proper, permits Kaplan s account to predict that a sentence such as I am here now is valid (in this indexical sense) yet not necessarily true. By analogy, if relevant constraints were imposed on the models here (for example, if the only contexts considered were contexts where any referent of Paul R is in the extension of Paul P ), my account would also render IF1 valid in this indexical sense, without thereby predicting that it is necessarily truth preserving, i.e. there would still be possible worlds where the referent of Paul R is not called Paul.

18 ANDERS J. SCHOUBYE entirely clear what that explanation is supposed to be. But, to further bolster the case for my proposed analysis (and the explanation proposed above), consider the inference in IF3 below. He is tired So, at least one male individual is tired IF3 This inference looks parallel to IF1, i.e. it is intuitively an instance of perfectly good reasoning, yet it is not necessarily truth preserving (i.e. there might be possible worlds where the referent of he in the context is not male). One natural explanation of the intuitive correctness of this inference would now be identical to the explanation for IF1, namely that the φ-features associated with the pronoun constrains what that pronoun can be used to refer to. Consequently, if He is tired is true in a context c, the pronoun must then refer to an individual who is male in c. In short, the conclusion straightforwardly follows. It is natural to assume that the referential terms in IF1 and IF3 have semantically restricted uses, i.e. Paul can only be used to refer to individuals called Paul whereas he can only be used to refer to individuals who are male. These two assumptions are what permit a straightforward explanation of the intuitive correctness of the inferences. So, given the similarity between IF1 and IF3, it seems quite reasonable to assume that they have similar explanations. Yet, if the Millian is correct, IF1 and IF3 will likely have fundamentally different explanations: IF1 must be explained without any assumptions about the meaning of the name, whereas the explanation of IF3 would naturally rely on the pronoun s semantic association with φ-features. The question then is what reasons there are for assuming that these explanations should be fundamentally different. Next, Competence (E2). To account for the previous observations concerning competence, notice two things: (a) pronouns also have predicative uses, i.e. uses as count nouns, and (b) the observation about competence with respect to proper names also extends to pronouns. For example, a speaker who is capable of understanding the use of she in (27a) is also typically capable of understanding the use of she in (27b) and mutatis mutandis for the sentences in (28a) (28b) and (29a) (29b). (27) a. My kitten, she loves music. b. Oh, your kitten is a she? (28) a. There s one male and one female snake in every cage. b. I see. Is that the she? (29) a. HE is a bit aggressive, but SHE is such a cute little monkey.

Type-Ambiguous Names 19 b. I think you are confused. Both of my kittens are shes. 31 What explains this observation? The best candidate explanation is intuitively that competent speakers are capable, somehow, of drawing connections between (a) the content of the φ-feature constraint associated with the pronoun (the restriction on gender) and (b) the property expressed by the predicative use of the pronoun, namely the property of being female. In short, the most plausible explanation is that a speaker who understands that she can refer only to female individuals somehow infers that the relevant salient property with regards to predicative uses of she, i.e. attributions of the form is a she, is the property of being female. 32 Admittedly, this leaves an important question unaddressed, namely what it is, i.e. what mechanism it is, that enables the hearer to draw these inferences? That is a difficult question, but in all likelihood also a question whose answer should explain similar observations about many other expressions, e.g. the examples below. (30) a. I grabbed a bottle. b. Could you bottle the wine? (31) a. Is the book on the shelf? b. Yes, I shelved the books earlier. (32) a. Here s some shampoo. b. Great. I ll shampoo Rex later. (33) a. Did you see the ship? b. No, I was shipping your gift. If a speaker understands (30a), she also typically understands (30b) or at the very least is capable of inferring its meaning. The same holds, mutatis mutandis, for the other pairs above. The general feature common to the examples in (30) (33) is that the emphasised expressions in the (b)-sentences are morphologically derived from the emphasised expressions in the (a)-sentences and that their lexical categories are changed in this process. A morphological derivation is, roughly speaking, a process by which a derivational affix (so, a prefix, infix, or suffix) is added to an expression resulting in a different expression having a distinct but related meaning. A simple 31 An extensive list of examples of predicative uses of pronouns can be found in e.g. the Oxford English Dictionary (3rd edition, September 2013). 32 A referee for this journal raises a couple of worries for the parallel with pronouns. First, unlike names, pronouns cannot occur NP-internally in English, cf. *every she, *most shes, and *three shes. This is correct and it is not entirely clear to me why that is. It could be an accidental feature of English since there are other languages with predicative uses of pronouns that do allow NP-internal occurrences, e.g. Danish. The referee also notes that it is only third person pronouns that permit these predicative uses. Assuming that this is correct (which I do not think is obvious), there might be an explanation: In English (and probably various other languages) only predicates whose meaning relates to gender have been morphologically derived from pronouns. For example, to say that a cat is a she is to say that it is female (not that it is neither the speaker nor the addressee or that it is a singular individual). So, since only third person singular pronouns are marked for gender in English, only these can be used as predicates.

20 ANDERS J. SCHOUBYE example is the morphological derivation of a plural count noun from a singular count noun which normally requires only the addition of the suffix -s. However, some morphological derivations produce no morphological changes and these are standardly referred to as zero-derivations or conversions. As an example, consider the derivation of the verb to bottle from the common count noun bottle. As in the examples in (30) (33), this is also an example of a morphological derivation that has the effect of altering the lexical category, viz. one derives a verb from a noun. These kinds of processes, e.g. the process by which a noun is converted into a verb (through morphological zero-derivations), are extremely common in English and thus, in a technical term, said to be productive. 33 In light of examples such as (30) (33), it seems natural to draw the following general conclusion: competent speakers are endowed with an ability to immediately understand or infer the meaning of an unfamiliar expression if it is morphologically derived from an already familiar expression. But, again, what would explain that speakers have this ability with respect to morphologically derived words? The only plausible explanation is essentially the explanation outlined above, namely that the derived word shares some crucial component of meaning with the word from which it was derived. Hence, the reason that a speaker will understand the meaning of the verb to bottle when the speaker is only antecedently competent with the common count noun bottle is that one is derived from the other. That is, the meaning of the verb is essentially related to the meaning of the noun, and this overlap in meaning is what enables understanding (and thus explains competence). With regards to names, notice that their behaviour (intra- and cross-linguistically) looks similar to the behaviour of pronouns. So, whatever explains the observation about competence with respect to pronouns, that explanation could also potentially explain the observation about names. In both cases (given my analysis of names), there is a similar overlap in content between the referential terms and their predicative counterparts, and it seems plausible that this is precisely what explains why someone competent with the referential uses of she or Paul are also competent with their respective predicative uses. Finally, the worries about Intra- and Cross-Linguistic Uniformity (E3): First, why are all names in English (and not merely some names) type-ambiguous? Consider again the explanation of competence suggested above. That explanation assumed that speakers are capable, somehow, of drawing inferences from (a) the content of the φ-features of a name (or pronoun), to (b) the property expressed 33 The notion of productivity in linguistics is used to refer to grammatical (e.g. morphological) processes that are preferred for new expressions. For example, in English, the suffix -ed is the preferred morpheme for past tense even though there are alternatives. So, the process by which the morpheme -ed is added to a verb to indicate past tense in English is productive. My claim here is that with regards to both pronouns and names, there is a similar process (viz. a conversion or a zero-derivation process) by which pronouns and names are converted into predicates and that this process is productive not only in English but also in other languages.

Type-Ambiguous Names 21 by the predicative use of that name (or pronoun). Therefore, a speaker who understands that Paul can refer only to individuals called Paul is capable of inferring that the relevant property with regards to various constructions, for example determiner phrases such as some Paul or both Pauls, is the property of being called Paul. In short, the predicative name is morphologically derived from the referential name. If this explanation is correct, it is then completely unsurprising that the ambiguity applies to names in general, because it would be inexplicably arbitrary if the ability to draw such inferences was restricted to only some names. Second, what would explain that the type-ambiguity is attested across such a wide variety of other languages? Proponents of The Predicativism often emphasise the ubiquity of predicative uses of names across other languages, but it is rarely noted that the languages where predicative uses of names are attested also often exhibit important differences in their distribution, i.e. in the varieties of predicative uses that are possible. To give just one simple example, while names can be used predicatively in Scandinavian languages such as Danish, Norwegian, and Swedish, the predicative uses are much more limited than in English. Names in these particular Scandinavian languages do not generally take plural morphemes and predicative plural names are, as a result, almost invariably judged ungrammatical. Moreover, in Danish, definiteness marking is achieved using either free-standing articles (den, det) or suffixes (-en, -et). However, names in Danish cannot take any of the definite suffixes, so names in Danish differ importantly from common count nouns in that these generally accept definiteness marking using suffixes. 34 So, what could explain these cross-linguistic differences? While one should be careful about drawing general conclusions from what might be considered anecdotal observations, suppose for the sake of argument that predicative names in English are morphologically derived from referential names. That is, suppose that English contains a count noun, Paul P (lexical category NP) and that this has been derived through a lexical category changing conversion from a referential expression, Paul R (lexical category DP). Suppose further that the expression Paul R has the semantics given in (25). If this were the correct explanation of how predicative names come into existence, i.e. via morphological zero-derivations, one should then expect to see variations across various languages. For example, one should expect that languages that are conservative with regards to, say, derivations that change lexical categories might have fewer uses of predicative names compared to languages that are very liberal with respect to such derivations. If so, it would make sense that a liberal language such as English would permit plural uses of predicative names whereas a less liberal language such as Danish might not. In other words, one might expect to 34 There are interesting distributional facts about when common nouns take a free-standing article versus a suffix, see e.g. Hankamer and Mikkelsen (2002) and Matushansky (2006) for discussion, but that does not change my point here. Contrary to normal count nouns, names in Danish never take definite suffixes -en or -et.

22 ANDERS J. SCHOUBYE see differences that are in actual fact attested. In contrast, suppose that names are uniformly predicative (as The Predicativists maintain). If so, should it not then seem surprising that there are languages where such allegedly simple count nouns just cannot be pluralised. Why would that be and what would explain it? 35 The more general point is that predicative uses of names in other languages (and variations across these languages) are compatible, and indeed expected, on the specific type-ambiguity view defended here. Moreover, to suppose that names are ambiguous in other languages is neither ad hoc nor unprincipled when one can systematically explain how and why this ambiguity would have arisen. With typeambiguous expressions there is a very simple and plausible explanation, namely that the ambiguity arises as a result of morphological zero-derivations. And if this is correct, this provides a nice foundation for explaining facts about competence. Hence, the best answer to the question why is the ambiguity cross-linguistically uniform? is that it is useful! Clearly, if a language has referential names, it would most likely be useful for speakers of that language to also have a predicate that expresses the property of being called that name. So, if the language is sufficiently liberal with regards to derivations that change lexical categories (i.e. if those processes are productive in a language), it is entirely unsurprising that predicative uses are ubiquitous. Moreover, the same argument applies in the case of predicative uses of pronouns (which are also attested in other languages, e.g. Danish, Norwegian, Swedish). 2.4 Conclusion If referential names are analysed as a species of pronoun, the standard objections to the view that proper names are type-ambiguous are easily dismissed. Moreover, 35 A referee for this journal challenges this explanation on the following grounds: Once the lexical entry for a predicative name is established, it should not be subject to non-standard constraints, e.g. a restriction against pluralisation. As a result, the lack of plural uses of names in e.g. Danish is as much of a problem for my proposed view as for The Predicativism. This is a good point. My only very tentative response would be that the distributional facts about plural predicative names seem more surprising if names are assumed to be uniformly predicative. Whereas, if they are the result of some morphological derivation, I find it easier to believe that various language internal rules might then kick in to block further derivations, e.g. pluralisation. But, admittedly, this is not an entirely satisfying explanation. Similarly, the referee also notes that if it assumed that there are predicative names, but moreover that the is never phonologically null (which I am assuming), an explanation is then needed as to why descriptions such as the Paul or the Mary are infelicitous. Again, I do not at present have a good explanation, but I am tempted to suggest that the reason is that there is no need for such descriptions. Their obvious use is covered, so to speak, by the referential names. Moreover, this seems to be a problem not just for me, i.e. the corresponding question for the proponent of The Predicativism would be why the determiner must be phonologically null when occurring in front of name?

Type-Ambiguous Names 23 there is a plausible and systematic explanation of the ambiguity available and this explanation fits nicely with independent observations about e.g. pronouns. For that reason, positing a type-ambiguity is neither ad hoc nor does it add gratuitous theoretical complexity. Finally, because there are strong similarities between pronouns and names, i.e. both have referential and predicative uses, are productive, license various inferences, the proposal to analyse names as a type of pronoun is justified and provides its own kind of theoretical unification. In other words, there are compelling reasons for preferring the type-ambiguity view. This now leaves us in the following dialectical situation: If referential names are construed on the model of pronouns, the thesis that names are type-ambiguous is strongly supported, principled, and thus perfectly feasible. However, the typeambiguity view does commit us to an ambiguity. 36 However, since The Predicativism needs not posit an ambiguity in proper names, proponents of this view might insist that this is a simpler view, and hence a theoretically more parsimonious view. That would only be correct if The Predicativism and the type-ambiguity view were equal in all other respects. The remainder of this paper is devoted to demonstrating that this is not the case. Indeed, proponents of The Predicativism need to make several problematic assumptions in order to adequately capture the meaning of referential names. 3 The Perils of The Predicativism Even if it is granted to the proponents of The Predicativism that it is, ceteris paribus, a theoretically simpler view, the problem for The Predicativism is that it comes with a number of additional costs. In short, all things are not equal between my version of the type-ambiguity view and The Predicativism. 3.1 Referential Names and Rigidity The Predicativists generally endorse the following three theses (or something very close), cf. Fara (2015b, 97). C1 Predicative Names A name, for example the name Paul, is a multiply applicable predicate that applies contingently to an individual only if that individual is called Paul. C2 Covert Definite Determiners When the name Paul appears as a bare singular in argument position of a predicate, the name is the sister of a covert and unpronounced definite article the. 36 In the following sense: it requires an expansion of the lexicon two separate lexical entries for each name (just like there are two separate lexical entries for the verb bottle its noun counterpart).

24 ANDERS J. SCHOUBYE C3 One Definite Determiner There is only one definite determiner the, however it can occur either overtly or covertly (viz. pronounced or unpronounced). Given these assumptions about the meaning of proper names, one immediate worry is how proponents of The Predicativism are going to capture the fact that referential names are rigid and fixed. Since The Predicativism assumes that referential names are definite descriptions of the form The N where N is an occurrence of that name and since descriptions are not generally rigid, proponents of The Predicativism need some way of predicting that a certain class of definite descriptions are in fact rigid, namely the descriptions where the argument of the definite determiner is a name. The central question, of course, is how The Predicativists are going to achieve this result without simply making ad hoc provisions specifically for names. 37 For example, were one to assume that count nouns that are of the name-variety just happen to give rise to rigidity when combined with a definite determiner, one would need independent justification for that assumption. Without such independent justification, it would simply be stipulative and thus not suffice as an explanation for why names are rigid. 3.1.1 Elbourne (2005) and Matushansky (2008) on Rigidity While Elbourne s (2005) and Matushansky s (2008) views are importantly different, their analyses both assume that referential names are associated with some kind of indexical or context-sensitive element. For example, Matushansky writes: A possible account for the rigidity of proper names comes from the widespread proposal that it results from indexicality, since indexicals such as I, now or here are also known to denote the same individual across different possible worlds. (Matushansky, 2008, 599) Specifically, both analyses assume that when a proper name (i.e. a count noun) is composed with a definite determiner, the resulting definite description contains a variable whose semantic value is contextually determined. Where Elbourne s and Matushansky s accounts differ is in their assumptions concerning the nature and the structural location of this indexical element. On Elbourne s view, the LF associated with a bare singular occurrence of Alfred in argument position of a predicate is (34) where the definite determiner is unpronounced. Given this LF, a variable assignment g, and assuming the presupposition 37 One, it seems to me unexplored, possibility would be to consider so-called descriptions that have grown capital letters, e.g. the Holy Roman Empire or the Space Needle. These exhibit paradigmatic name-like behaviour but seem syntactically a kin to definite descriptions. Thus identifying the feature of these descriptions that make them behave like names could potentially be a step in the right direction. For discussion (yet no answer to this particular question), see Rabern (2015).

Type-Ambiguous Names 25 of the description is satisfied, its semantic value will then be (35), cf. Elbourne (2005, 172-178). 38 (34) [[THE 2] Alfred] (35) ιx.[alfred(x) x = g(2)] Elbourne provides independent justification for the existence of the index i (i = 2 above), cf. (2005, 95-97, 112-115), which functions as an (additional) argument of the definite determiner. However, Elbourne distinguishes three types of uses of definite descriptions, namely bound uses (the uses that initially motivate associating an index with the determiner), referential uses, and attributive uses. 39 In cases where the description is used attributively, the index is effectively vacuous (Elbourne uses the number 0 for this type of case). Given Elbourne s analysis, a referential use of the description the murderer expresses the following e-type content: (36) [[the 1] murderer] g = ιx.[murderer(x) and x = g(1)] That is, relative to a variable assignment g, the semantic value of the description is an individual, specifically the unique individual who is a murderer and identical to g(1). The presupposition associated with the description will ensure that there is such an individual (or the description will have no semantic value), and the identity condition will then in turn ensure that the description is rigid i.e. the individual denoted by this description will be g(1) even when embedded under modal or tense operators. In contrast, if the index 0 is in play, the description expresses the following e-type content: (37) [[the 0] murderer] g = ιx.[murderer(x)] The denotation of this description is also an individual, but its content does not essentially involve a specific individual. This means, when used attributively (with the vacuous index 0), the description is not rigid. Given this analysis, Elbourne s account is supposed to capture the rigidity of proper names as follows: When a bare singular name occurs in argument position of a predicate, it is simply a covert definite description whose index is unbound and non-vacuous. In short, bare singular names in argument position of a predicate (viz. referential names) are e-type expressions that contain a referential index which fixes the referent. As a result, the referent will not shift across possible worlds, and the descriptions are thus rigid. 38 This is notation used by Elbourne (2005). Unlike Russell s original use of the ι-notation, the ι-expression is here a singular term referring to the unique individual x such that x is called Alfred and x is identical to g(2). 39 Roughly, referential and attributive in the sense proposed by Donnellan (1966).

26 ANDERS J. SCHOUBYE In contrast to Elbourne, Matushansky (2008, 599) proposes the following lexical entry for the name Alice. (38) Alice = λx: x D e. λr D e, n,t. R(x)(/ælIs/) In this lexical entry, the variable R ranges over naming conventions. The naming convention is a relation between an individual (the individual named) and a phonological string (the individuating criterium for a name). In constructions containing a naming verb, the argument for the naming convention is supplied by the verb, cf. Matushansky (2008, 594-595). Using this lexical entry for names, the explanation for the rigidity of referential names is the following: In order to account for the rigidity of proper names in argument positions I propose to compare proper name predicates with relational nouns like friend and adjectives like local and close, which may take a contextually supplied indexical as an argument. [...] Extending this analysis to proper names, we hypothesise that in argument positions the naming convention argument slot is saturated by a free variable that of the naming convention in force between the speaker and the hearer, or more strictly speaking, the naming convention of the speaker that is presupposed to be shared by the hearer. This convention (I will indicate it as R 0 ) is indexical in the sense of being fully extensional: it contains no argument slot for a possible world. As a result, proper names in argument positions will be rigid. (Matushansky, 2008, 599) So, the denotation of the name Alice when occurring in argument position of a predicate is the following: (39) the Alice = ιx. R 0 (x)(/ælis/) where R 0 is the naming convention in force between speaker and hearer in the context of utterance. The ι-expression in (39) is, again, an e-type expression (a referential term) that can be informally read as the unique individual x such that x is called /ælis/ by the contextually determined naming convention in force between the speaker and the hearer. Since R 0 is a contextually determined naming convention, i.e. the value of an indexical, the definite description refers only to the individual named /ælis/ by that specific naming convention. Since only one individual can be so-named by the specific naming convention in play in the context of utterance, this entails that the description the Alice determines a specific individual that does not vary across possible worlds. In short, the name is rigid. It thus seems that both Elbourne s and Matushansky s accounts are perfectly capable of capturing rigidity. So, what is the problem? The problem is that both these accounts capture the rigidity of referential names by relying on unjustified and ad hoc assumptions. For Elbourne, this is the assumption that the index associated with the definite determiner is never (or very rarely)

Type-Ambiguous Names 27 vacuous (i.e. 0) when the count noun that composes with the determiner is a name. Elbourne attempts to justify this assumption as follows: [...] any use of a proper name in which the speaker does have some specific person in mind and intends to refer to that person is ipso facto a use that employs one of the nontrivial indices, and it is hard to construct circumstances in which a speaker might use a proper name and not intend to refer to some specific person they have in mind. They would have to be in a position to know that that name was appropriate even though they know nothing about the person that would enable them to refer to them, and this seems contradictory. (Elbourne, 2005, 174) However, this explanation seems to get things backwards. To observe that it is difficult to use a name like one would use a description is just labelling the problem that needs explaining. If bare singular names simply are covert descriptions, then why would it be difficult to use such a name in the way that one would use a description? For example, one can easily use a description such as the murderer to refer to an individual where the only information available about the referent is that he/she is a murderer. So, if names are count nouns on a par with murderer, why should there be a difference with respect to names. This is the question that needs to be addressed. The general point is that for the predictions about the rigidity to come out as desired, Elbourne must make special provisions for names, i.e. assume that names are different from other count nouns which readily permit the 0 index. However, a question then arises, namely how is this better than simply assuming that names are (type) ambiguous? It simply is not. It is affording special status to names that effectively set them apart from count nouns and as far as theoretical parsimony is concerned, this is equivalent to positing some kind of ambiguity. 40 An analogous problem afflicts Matushansky s explanation of rigidity. Remember, Matushansky assumes that when a name is in argument position of a predicate, the naming convention is then indexical in the sense of being fully extensional and as a result [...] names in argument positions will be rigid (2008, 599). The question is what would justify this assumption? It is quite clear that when names occur in other syntactic positions, making this assumption is not feasible. For example, when a name is used predicatively, e.g. as the syntactic argument of a quantificational determiner, this assumption leads to incorrect predictions. To illustrate, cf. (40). (40) It s possible that every Alfred is blonde. 40 There is a sense in which it really just is ambiguity it is simply ambiguity at the level of the definite determiner. I.e. one could redescribe Elbourne s view as follows: There are two definite determiners, one which has an index that is sensitive to the variable assignment and one with no index (or alternatively a void/null index which is thus not sensitive to the variable assignment).

28 ANDERS J. SCHOUBYE (40) has a reading where, assuming a simplified semantics for modals, it is true at a world w iff there is an accessible world w from w such that every individual called Alfred at w is blonde. In other words, (40) has a reading where every Alfred takes narrow scope relative to the modal. But capturing this requires that the naming convention is not fully extensional and can vary across possible worlds. If it cannot, this then forces the equivalent of a wide scope reading of the determiner phrase, namely a reading where (40) is true at w iff there is an accessible world w from w such that every individual called Alfred as a result of the naming convention established in w is blonde. This point could be extended to more or less any other determiner phrases, e.g. some Alfred, most Alfreds, three Alfreds etc. In other words, when a name is the syntactic argument of a determiner, the naming convention should not (invariably) be a fully extensional indexical whose value is determined by context. Indeed, this point can even be extended to the definite determiner when this determiner is combined with a modified name, e.g. the Jack from Texas. Such a definite description will also exhibit variable narrow scope readings. However, it appears that we should allow one special exception to this rule, namely when a (unmodified) name is the direct syntactic argument of the (covert and unpronounced) determiner the, then it seems that the naming convention should be such a fully extensional indexical. Why? Because referential names are rigid. The problem with this explanation is basically analogous to the problem discussed above. For Matushansky s account to make correct predictions, she must assume that names are special. Specifically, names must be a type of count noun that exhibits a very peculiar behaviour whenever composing with a definite determiner (in argument position of a predicate). In such constructions, the naming convention associated with the name somehow becomes an indexical whose value is determined by context and this ensures rigidity. But, again, how is this an improvement over the assumption that names are ambiguous? In both cases, names are treated not as simple count nouns, because in both cases names are assumed to differ from count nouns in important respects. In more general terms, the main point is this: If you propose a reductive analysis where expressions of a certain type N (e.g. names) are argued to simply be instances of a general category of expressions of type CN (e.g. count nouns), the onus is on you to provide an explanation why the particular expressions in N seem to display semantic behaviour that the other expressions in CN do not. If you attempt to explain this non-standard semantic behaviour of the expressions in N by simply assuming that these expressions have semantic properties that other expressions in CN do not, this provides some justification for thinking that the reductive analysis was perhaps wrong to begin with. Possibly, expressions of category N are just not the same semantically as expressions of type CN. Certainly, if the main argument for proposing a reductive analysis to begin with was overall theoretical simplicity i.e.

Type-Ambiguous Names 29 having one category of expressions is simpler than two then the ad hoc assumptions needed to explain non-standard behaviour would seem to, at the very least, cancel out whatever putative theoretical advantages that the increased simplicity was supposed to provide. A referee for this journal notes that Fara (2015b) rejects this kind of argument on the grounds that even within the category of nouns, there are non-trivial distributional differences. If one is to maintain that mass terms are nouns despite their syntactic and semantic differences from count nouns, then one should have an independent criterion for being a noun and show that mass terms satisfy that criterion. [...] Likewise, if one is to maintain that names are count nouns, then one should have an independent criterion for being a count noun and show that names satisfy that criterion. Things are better if we can also make some diagnostic generalisations about the syntactic differences between names and common count nouns. In the case of mass terms, we can make a number of syntactic generalisations. Mass terms cannot complement the determiners a or every ; they cannot occur in the plural; they cannot complement how many, but they can complement how much. We will see that the -predicativists can make correspondingly predictive generalisations about names as compared with common count nouns. (Fara, 2015b, 77-78) Following (Sloat, 1969, 27), Fara observes that with respect to names and common count nouns, the distribution of determiners is basically identical. Indeed, it is only with respect to the that there seems to be differences, namely the following: The tiger ate. *Tiger ate. *The Paul ate. Paul ate. Simplifying somewhat, Fara follows Sloat in assuming that the simplest explanation for the distributional facts about the is that it can occur covertly in certain contexts. On the basis of an extensive analysis of the distribution of the with names (where Sloat s original chart is revised in important ways), Fara then formulates a simple generalisation which is supposed to predict the distribution of phonologically null occurrences of the. Facts about this distribution then serve as evidence for the assumption that names are uniformly count nouns. That is, what the distributional evidence suggests is that in cases where a name might seem to be something other than a count noun, it is in fact the sister of an unpronounced definite determiner. Fara s argument is rather elaborate, so I will not discuss it in detail here. However, let me just make two short observations. First, note that since this argument relies extensively on the Sloat chart, i.e. observations about the distribution of determiners in English, the argument is somewhat anglocentric. There are numerous

30 ANDERS J. SCHOUBYE languages where the distribution of determiners with respect to names and common count nouns looks nothing like the Sloat chart, e.g. Scandinavian languages such as Danish and Norwegian. The question is thus whether Fara s argument for names being uniformly count nouns will work when such languages are taken into consideration. Second, even if Fara s argument is correct, this fails to account for the fact that whenever the definite determiner occurs as phonologically null (and hence is the sister of a name), the resulting description must somehow be rigid. This must be stipulated which is essentially what both Elbourne and Mathushansky do. In fairness, Fara (2015b) seems aware of this problem and therefore attempts to account for rigidity in an alternative way. This is discussed in the following section. 3.1.2 Fara (2015b) on Rigidity and Incomplete Descriptions A better attempt at an explanatory account of the rigidity of proper names, assuming that names are count nouns, is given by Fara (2015b). First, Fara points out that bare singular names in argument position of a predicate are in fact (covert) incomplete descriptions. This seems unobjectionable; since there is more than one individual called Paul, a description of the form the Paul which is semantically equivalent to something along the lines of the x such that x is called Paul fails to determine a unique individual, and hence that description is incomplete. Second, Fara conjectures that incomplete descriptions are rigid-in-a-context where this means that the expression can refer to different things in different contexts, but is rigid once context has fixed its semantic value. Consider, for example, (41). (41) Olga enjoyed the party. Fara writes: If you were to sincerely utter [41] you would be talking about some one particular party call it BASH and saying of it that Olga enjoyed it. Suppose that the utterance is true: that Olga did in fact enjoy BASH. Someone who overhears your utterance of [41] might well not know what party you are talking about. If he asks you, what party are you talking about? you might say, Naomi s 40th birthday party. Or you might equally satisfyingly respond by saying the party I went to last night. Since your aim is to enable your audience to know which of the many parties that happened last night is the one that you are talking about, it is appropriate to give any answer that will adequately convey to your audience which party it is that you are talking about. Nothing in such exchanges requires that there be some one particular completing description that enters into the proposition expressed by your original utterance of [41]. When you use the incomplete description the party, you use it to talk about a particular party, to say something about it as opposed to whatever party is the so-and-so (as Donnellan (1966) might have put it) where is the so-and-so is supposed to stand in for some particular completing description recovered from the context. (Fara, 2015b, 97-98)

Type-Ambiguous Names 31 In the quotation above, Fara appears to be advocating the view that the semantic value of the incomplete description the party in (41) is simply the specific party to which the speaker intended to refer. That is, one could interpret Fara as here assuming that the only propositional contribution of the description is an individual (so the description is effectively an individual constant). If so, this would straightforwardly account for the purported rigidity of incomplete descriptions. 41 Notice that if Fara is right, this would capture the rigidity of referential names in a perfectly principled way. If incomplete descriptions are rigid, rigidity is then simply a property of a certain subclass of descriptions regardless of whether the restrictor of that description is a name. This would be a significant improvement over Elbourne and Matushansky. 3.1.3 Incompleteness, Scope, and Rigidity Rather than accepting that incomplete definite descriptions are referential in the sense described above, the standard alternative response is to maintain that these descriptions are in fact, and contrary to immediate appearances, complete. For example, one could argue that when e.g. (41) is asserted in a context, it expresses something like (42). (42) Olga enjoyed the party that I went to last night. 41 Fara does, however, explicitly deny that she is committed to any particular way of capturing the rigidity of incomplete descriptions: [...] there is no onus on me to provide an explanation of how or why incomplete descriptions are rigid designators. That is the right of the piggybacker. I don t have to take a stand, for example, on what the mechanism is that renders incomplete definite descriptions rigid on whether, for example, rigidity requires a covert actually operator or whether, alternatively, there is more than one definite article [...] (Fara, 2015b, 102-103) However, it is not entirely clear how, say, a covert actuality operator fits with what Fara says in the quotation above. An actuality operator would make the description rigid, but it would not generally solve any incompleteness issues. For example, a description such as the x such that x is actually called Paul would still fail to pick out a unique individual and hence still be incomplete. In other words, unless the description is assumed to refer, as in directly refer, to a particular individual (given that it is incomplete), a sentence containing that description just does not seem to succeed in expressing a proposition. Having more than one definite article could help resolve the incompleteness issue, but would also effectively amount to adopting a semantic distinction between attributive and referential descriptions, which is not exactly uncontroversial for discussion see e.g. Neale (1990), Bach (2004), Schoubye (2012). However, if Fara thinks that proper names are covert incomplete descriptions, explaining why speakers actually succeed in expressing propositions when using names seems as important as explaining why the names are rigid. Assuming that incomplete descriptions are directly referential terms (which is what Strawson (1950) seemed to think) would help explain both, and it is not clear what other account of rigidity could really work here.

32 ANDERS J. SCHOUBYE This type of proposed explanation, however, raises various questions, e.g. what determines the expanded content of (41), i.e. the relative clause modifying party, and what is the syntactic and semantic status of this expansion? Fara considers, and in turn rejects, three proposed explanations for why incomplete descriptions are in fact complete. V1 DOMAIN RESTRICTIONS Sentences can be evaluated in restricted domains which are determined by the context. Hence, a sentence such as (41) might be evaluated relative to a domain D where the only party in D is a party that I went to last night. V2 ELLIPSIS An incomplete description is elliptical for a richer and complete description. V3 CONTEXTUAL COMPLETIONS Common nouns, e.g. party, are equipped with a syntactically associated variable that denotes a property. In context, this variable is assigned a value, e.g. {x x is an event I attended last night} and this property is then intersected with the property denoted by the noun, e.g. {x x is a party} yielding the semantic value of the noun in context, viz. the set of things that are parties and that I attended last night. Fara immediately dismisses V1 because, as she points out, this analysis is unable to deal with so-called mixed-domain cases, e.g. (43). (43) The dog got in a fight with another dog. McCawley (1979) If the domain of (43) is restricted to just one dog (so as to guarantee that the definite description in subject position refers), there is then no plausible interpretation of the determiner phrase in object position, viz. another dog. Hence, the domain restriction strategy fails. 42 With regards to V2 and V3, Fara argues against both by considering the behaviour of incomplete descriptions in modal contexts. Compare (44) and (45). If one assumes either the ellipsis view or the contextual completions view, then (44) would, relative to some context, be truth conditionally equivalent to (45). (44) Olga might have enjoyed the party. (45) Olga might have enjoyed the party that I went to last night. It is generally accepted that definite descriptions can take either narrow or wide scope with respect to modal operators, so (45) should have two possible readings (which, according to Fara it does), namely (45a) and (45b): 42 Fara is quick to dismiss V1 but for reasons of space I cannot discuss the merits of this view here. However, I will just mention that as long as one is willing to divide up the domain, or alternatively introduce new domains or subdomains, there might be ways to deal with mixed-domain cases. Thanks to Torfinn Huvenes for discussion here.

Type-Ambiguous Names 33 (45) a. It might be that Olga enjoyed the party that I went to last night. b. The party that I went to last night is an x such that it might be the case that Olga enjoyed x. But Fara maintains that (44), in contrast to (45), has only one reading, namely the wide scope reading in (45b). On the basis of this claim, she concludes: In other words, [44] has only the truth conditions that it would have if the incomplete definite description were rigid. Since incomplete definite descriptions such as the table or the party can be used to talk about different tables or parties on different occasions, it is right to say that these definite descriptions are rigid-in-a-context. (Fara, 2015b, 100) In short, the rigidity of referential names, that is bare singular names in argument position of a predicate, is explained by the fact that when composed with a covert and unpronounced definite determiner, the result is an incomplete definite description and such descriptions are rigid-in-a-context. There are, in my view, several significant worries with Fara s argument above. First, while it might be granted that a wide scope reading of (44) is the most natural reading, the conclusion that incomplete definite descriptions consistently take wide scope is just false. This is very easily demonstrated by considering a simple variant of (44). Suppose Olga comes home from a party and is looking particularly hung over. You now say, (46) Olga must have enjoyed the party! You can clearly felicitously assert (46) without having any specific party in mind nor referring to a specific party after all, Olga might have had a range of parties to choose from and you might not be aware which of these she decided to attend. However, for that interpretation of your utterance to be available, the description the party must take narrow scope with respect to the modal. In other words, on this reading, the referent of the party varies across the points of evaluation and so, the description is non-rigid. In short, even if the wide scope reading of (46) is strongly preferred, a semantic analysis is adequate only if it has sufficient resources to predict that (46) also has a narrow scope reading. Fara dismisses V2 and V3 by arguing that these approaches wrongly predict that a sentence such as (46) has at least two readings, but this is a reason to favor, rather than dismiss, these views. The problem for Fara, of course, is that if incomplete descriptions have non-rigid readings (possibly because they are not incomplete in context), it then remains an open question why, if the description was substituted for a name, the name would only have a rigid reading. If names are covert incomplete descriptions, they should behave like incomplete descriptions, yet they do not.

34 ANDERS J. SCHOUBYE A closely related problem for Fara s explanation of rigidity is the fact that many incomplete descriptions are naturally used attributively. To illustrate, suppose Mary asks her assistant to get a rental car. Mary says (47). (47) The rental car should have four doors. 43 The definite description in (47) is incomplete, but on its most natural reading, it is not rigid. Indeed, Mary s use of the description appears to be attributive since she clearly has no particular car in mind. Moreover, it seems quite natural to interpret Mary as having asserted a slightly more specific proposition, e.g. the rental car that you end up renting should have four doors, or something along such lines. The non-rigidity of the description in (47) seems to be a prima facie problem for Fara s claim that incomplete descriptions are rigid-in-a-context. Fara attempts to dispel this worry by exploiting a distinction between role-type and particularised descriptions due to Rothschild (2007). According to Rothschild, a description is role-type if, [...] it is part of the common ground that there is exactly one person (or one salient person) satisfying the descriptive content across a range of relevant metaphysically possible situations and that the satisfier sometimes varies from situation to situation. Some examples of role-type descriptions are the family lawyer, the mayor, the president, the tallest pilot, and the director. With role-type descriptions, we usually know independently of the specific conversational situation that the descriptive content is satisfied uniquely across other possible situations: It is part of general knowledge that cities generally have one mayor, countries one president, and so on. (Rothschild, 2007, 75) Hence, according to Fara, the reason that the rental car in (47) is non-rigid is that it is a role-type description. In asserting (47), a speaker is simply characterising the properties that an object must have in order to play the relevant role. The reason that the rental car and the party can be used non-rigidly [...] is that they are being used as role-type descriptions that do not yet denote anything at all; we are deciding which things are going to fill the role and are invoking various criteria. (Fara, 2015b, 104) However, if incomplete descriptions generally have (non-rigid) role-type uses, then names should have role-type uses too. Indeed if Fara is correct that incomplete descriptions are rigid in just those environments in which a name would be (Fara, 2015b, 105), there should be no divergence in availability of role-type uses of names and descriptions as long as the environments in which these expressions occur are analogous. In support of the claim that names have role-type uses, Fara provides the following example. 43 Fara (2015b) attributes this example to Kent Bach via personal communication.

Type-Ambiguous Names 35 (48) Una should have been your first daughter. (As said to parents considering whether to name their second daughter Una.) According to Fara, the name Una is here used as role-type just like the incomplete description the rental car is in (47). I.e. the speaker is talking about the criteria that must be satisfied in order to fill the relevant role of the covert description. I must admit that I find (48) peculiar and bordering on infelicitous. However, setting that judgment aside, identifying one odd example of a name that appears, perhaps, to be used attributively and non-rigidly (viz. as a role-type description) is insufficient. Why is this insufficient? Because one can straightforwardly construct scenarios that are more clearly structurally analogous to (47) than (48), but where the names simply cannot be interpreted non-rigidly, viz. as role-type. Given this, an explanation is needed why names quite generally resist role-type interpretations in environments where incomplete descriptions do not. Indeed, this should just not be possible if, again, incomplete descriptions are rigid in just those environments in which a name would be. To demonstrate my point, consider again the context described earlier for (47). There, the background context was structurally the following: the speaker is looking for an x to play the role of F and then asserts that the F should be G. Now, consider the following: Mary has a strange obsession with people who are called Paul and therefore asks her assistant to invite someone who is called Paul to lunch. Mary now utters (49) to her assistant. (49) #Paul should have blond hair. While it is possible, in some sense, to understand what Mary is trying to convey by asserting (49), her use of the name is, at the very least, odd i.e. the assertion is bordering on infelicitous. 44 One natural explanation is that Mary is not intending to refer to a specific individual, yet the name can only be interpreted as such. So, in an environment such as (49) where the background conditions are structurally analogous to the context described for (47), i.e. the name is supposed to be role-type, it nevertheless resists a role-type (non-rigid) reading. However, if the name in (49) is really shorthand 44 With regards to (49), a referee for this journal raised two alternative examples that might support The Predicativism, namely the two below. (R1) (R2) Today s Paul should have blond hair. Paul should always/never have blond hair. However, as regards (R1), here the subject, Today s Paul, is a definite description (basically, the description The Paul of today ). So, the name Paul is functioning as a simple predicate (just as schedule is functioning as a predicate in Today s schedule ). As regards (R2), I must confess that, contrary to the referee, I find this sentence odd/marked in the same way as (49).

36 ANDERS J. SCHOUBYE for the incomplete description the Paul, then (49) should not sound odd. After all, why would it not be possible, as it was for (47), to interpret the incomplete description the Paul as being completed in context. In other words, why is it not possible to interpret Mary as having asserted something along the lines of the Paul that you end up inviting should have blond hair? Finally, these so-called role-type uses of descriptions are extremely easy to come by. For example, notice how easy it is to get non-rigid (and contextually completed) readings of the descriptions below. (50) [CONTEXT: Woman renting pony for a kids birthday] The pony should have blond hair. (51) [CONTEXT: Man buying fur for his wife and talking to store clerk] The fur should have blond hair. (52) [CONTEXT: Music video director looking for a girl to star in his video] The girl should have blond hair. In contrast, getting such role-type readings for names is extremely difficult, if possible at all. (53) [CONTEXT: Woman looking for a person called Barack Obama say for a documentary about having the same name as the president] #Barack Obama should be no more than 55 years old. It is hard to deny that there is a clear difference between incomplete descriptions and proper names. Compare (53) to the literally completed description in (54). (54) The Barack Obama for the documentary should be no more than 55 years old. It seems that implicit completions are not possible with a bare singular name yet perfectly possible with incomplete descriptions. So, if Barack Obama is shorthand for The Barack Obama why is an implicit completion similar to the one in (54) not possible? Again, this difference in behaviour needs to be explained. Summing up, the rigidity of names was to be explained by two assumptions, namely (a) that incomplete descriptions are rigid and (b) that referential names are a subset of the set of incomplete descriptions. However, it turns out that incomplete descriptions are not always rigid (e.g. when they are used as role-type), so Fara amends her thesis to say that incomplete descriptions are only rigid in those environments in which a name would be. Yet, what the examples above demonstrate is that this is simply false. In many environments where incomplete descriptions have non-rigid readings, names do not. A second, though less pressing, concern is that it is somewhat unsatisfying to be told that incomplete descriptions (which were supposed to explain the rigidity

Type-Ambiguous Names 37 of names) are rigid in just those environments that names are without then being told in which environments names are rigid. 3.2 Bare Singular Names vs. Incomplete Descriptions This leads me to consider a few of other general problems that proponents of The Predicativism (of all stripes) need to address. If names are count nouns which in an argument position of a predicate are composed with a covert and unpronounced definite determiner, the result (as Fara rightly observes) is an (incomplete) definite description. If this is the correct analysis of bare singular names in argument position of a predicate (i.e. referential names), one should expect the behaviour of such names to mimic the behaviour of incomplete descriptions in similar syntactic environments. I argued above, that with respect to rigidity, they do not behave the same. However, to make matters worse, there are other dramatic respects in which their behaviours differ. 3.2.1 One-anaphora The restrictor of an incomplete definite description can serve as an anaphoric anchor in cases involving so-called one-anaphors. 45 For example. (55) I left the duvet outside, but there is another one upstairs. We need not concern ourselves with the question regarding the correct analysis of one-anaphora, i.e. whether these kinds of occurrences of one should be analysed as pro-forms, dummy nouns, or perhaps instances of noun phrase ellipsis. 46 I introduce this kind of example only to demonstrate that as long as the restrictor of the incomplete description in the first conjunct is a count noun, the noun can then serve as anaphoric anchor for a one-anaphor. Given the assumption that names are count nouns, one would think that names should then also be capable of serving as anaphoric anchors. However, one-anaphora does not seem to be licensed if its antecedent is a name, cf. (56). (56) # I left Paul outside, but there is another one upstairs. (56) is straightforwardly infelicitous. It is just not possible to resolve the meaning of one and the most natural reaction to (56) would be to respond another WHAT is upstairs? 45 This observation is due to King (2006, 148-149). King s discussion focuses on the problem as it relates to That Predicativism, but it carries over more or less directly to The Predicativism. No proponent of The Predicativism has to my knowledge responded to this issue which is why I think it deserves to be mentioned again. Thanks to Paolo Santorio for bringing this type of example to my attention. 46 For discussion of this issue, see e.g. Llombart-Huesca (2002).

38 ANDERS J. SCHOUBYE One could argue that (56) sounds odd because no contextual setup is provided. I.e. the argument would be that when sentences such as (56) are asserted out of the blue, they just sound odd. The first thing to notice about this response is that (55) sounded fine yet no contextual setup was provided for that sentence. However, in order to accommodate this worry about the lack of a contextual setup, consider the following. Ann is meeting Jack at a restaurant. Since Ann has a strange obsession with men who are called Paul, Jack has promised to bring his friend Paul. However, as Jack pulls up to the restaurant, he notices that another one of his friends, also called Paul, is sitting in the upstairs section of the restaurant. He decides right then and there to leave the Paul sitting next to him in the car, and instead introduce Ann to the Paul who is eating upstairs. As Jack enters the restaurant, Ann greets him, and Jack then says: (57) # I left Paul in the car, but there is another one upstairs. Even with this highly elaborate setup, purposely designed to license anaphoric one, the sentence still seems infelicitous it remains a clear contrast to any standard occurrence of one anaphora. So, the problem for proponents of The Predicativism is that if names are count nouns, then some non-stipulative explanation is now needed as to why names cannot function as anchors for one-anaphors, and it is far from clear what that explanation would be. Of course, if referential names are e-type expressions (e.g. variables), one straightforwardly predicts that names should not license one-anaphora. 47 3.2.2 Attributively Distributed Descriptions Another general problem for The Predicativism is what I will refer to as attributively distributed descriptions. What I have in mind here are cases where an incomplete description occurs in the scope of some determiner phrase, but where that determiner, loosely speaking, is binding a variable associated with the description. This has the effect of neutralising the incompleteness associated with the description. For example, consider the cases below focus on the descriptions in boldface. (58) Sadly, every university professor in the country made the dean grade the classes. 47 A referee for this journal remarks in defence of The Predicativism that not all count nouns lend themselves immediately to one-anaphora. For example, I left the cat outside, but there is another one upstairs sounds quite odd. However, I think this is essentially an example of lacking contextual setup. To see this, note that it only takes a minimal amount of contextual setup for this sentence to sound perfectly felicitous. Just imagine that it is uttered in a context where someone needs a photo with a cat (any cat) in the background. In other words, despite nouns like cat, names seem resistant to one-anaphora in ways that count nouns generally do not.

Type-Ambiguous Names 39 (59) After this national scandal, at least one student at every school in the country filed a complaint with the student support officer. On the most natural readings of (58) (59), the incomplete descriptions (in bold) are used attributively and hence are neither directly referential nor rigid. Notice that to appropriately assert either (58) or (59) the speaker need not be acquainted with any of the possible denotations. The meanings of (58) and (59) can be more or less accurately paraphrased as follows. 48 (60) Sadly, [every university professor x in the country] made [the dean of x] (the dean at x s university) grade the classes. (61) After this national scandal, at least one student at [every school in the country y] filed a complaint with [the student support officer at y]. These descriptions are incomplete, but have very natural narrow scope readings where their denotations vary with a preceding quantifier. Since these are perfectly standard uses of incomplete descriptions, then if bare singular names are in fact covert incomplete descriptions, we should expect such occurrences of names to have attributively distributed uses too. So, let s see what happens if the incomplete descriptions in (58) and (59) are substituted for bare singular names. (62) Sadly, every professor in the country made Jack grade the exam. (63) After this national scandal, at least one student at every school in the country filed a complaint with Jack. The difference here is striking. The name Jack has only a referential interpretation in (62) (63). Now, granted, one might attempt to explain this by noting that there is also a crucial disanalogy between (58) (59) and (62) (63): To interpret the description in e.g. (59) as attributively distributed, it must be common ground that every school has exactly one student support officer, i.e. this must be antecedently established (or accommodated in context) in order for the co-varying interpretation of the description to be available. And since it is not common ground that there is precisely one individual called Jack at every school, the incomplete description in (63) simply cannot be interpreted as attributively distributed. Because of this, it is interpreted referentially (or so the argument would go). But again, this explanation is inadequate which can be demonstrated by considering what happens if we tweak the cases to avoid this issue. So, suppose for the sake of argument that there is exactly one individual called Jack at every school in the country now consider (64). 48 How to compositionally predict these meanings is a difficult question, but we need not be concerned with that here. Also, these are not simply cases of bound definite descriptions. I discuss this issue in the next section.

40 ANDERS J. SCHOUBYE (64) After this national scandal, at least one student at every school in the country filed a complaint with Jack. This does not seem to help. There is no reading of the name Jack in (64) where it is attributively distributed even when it is common ground (assumed to be true) that there is a unique individual called Jack at every school. So, the missing common ground information cannot be the whole explanation. Finally, to conclusively demonstrate that this really is due to a difference between proper names and incomplete descriptions, observe what happens when the name Jack is substituted for its alleged semantic correlate. Again, suppose that there is exactly one individual called Jack at every school in the country: (65) After this national scandal, at least one student at every school in the country filed a complaint with the person called Jack. Here, the description the person called Jack is easily interpreted as attributively distributed and this sharply contrasts (64). If, as proponents of The Predicativism maintain, these sentences, (64) and (65), are truth conditionally identical, viz. identical in meaning, there should be no differences in their possible interpretations, yet there clearly is. This is just another way of making the point that referential names behave in ways that are quite dissimilar from incomplete definite descriptions, and for that reason it seems highly doubtful that an analysis which treats referential names as covert incomplete descriptions could be correct. In short, it seems highly doubtful that any analysis along the lines of The Predicativism could be right. 3.2.3 A Quick Remark on Names and Binding There are multiple examples in the literature designed to demonstrate that names have bound (or co-varying) readings. So, just like the description in (66) appears to be bound (in the sense that its meaning co-varies with a preceding quantified NP), so do the names in (67) and (68). (66) If Carlos meets a scientist and decides to marry her, then his current wife will stalk the scientist and try to kill her. Fara (2015b, 105) (67) If a child is christened Bambi, and Disney Inc. hear about it, then they will sue Bambi s parents. (Geurts, 1997, 321) (68) If John insists on calling his next son Gerontius, then his wife will be annoyed and Gerontius will get made fun of because of his name. (Elbourne, 2005, 182) It is important to emphasize that the observation that names have bound readings has no direct bearing on the arguments above. What the previous argument

Type-Ambiguous Names 41 demonstrates is that there is a clear difference between the behaviour of a name Jack and its supposed semantic correlate the Jack or the person called Jack. There should not be such a difference if The Predicativism was correct. Finally, regarding binding of proper names more generally: This is obviously a complicated issue where the data, in my view, is less than clear. However, notice that an account that analyzes names as variables (i.e. pronouns) has resources to capture bound readings, see for example Dever (1998) and Cumming (2008). 49 In contrast, an analysis which treats names as constants, e.g. Millianism, does not. However, such resources do not come for free, because once the theory licenses binding of names, adequate binding constraints will then need to be formulated and justified. Since names show different binding behaviour than pronouns (i.e. names are generally less susceptible to binding), proponents of the view that I am defending here will need to provide some kind of explanation of this behaviour of names as opposed to pronouns. An entire paper could easily be devoted to a discussion of this issue, and for reasons of space, I am unable to engage in that discussion here. However, let me make two quick remarks on this issue. First, the extent to which pronouns can be bound varies quite dramatically across the standard category of pronouns. For example, it seems that third person pronouns are much more susceptible to binding than, say, first person pronouns. Second, this problem is equally a problem for proponents of The Predicativism since they assume that bare singular names in argument position are (covert) definite descriptions. However, definite descriptions are sometimes bound, but names are less susceptible to binding than definite descriptions, so The Predicativists are going to need an adequate explanation of this divergence in behaviour too. 4 Conclusion In conclusion, when names are analysed as type-ambiguous between predicates and pronouns, the resulting analysis has the following advantages: It retains the virtues of Millianism, but provides the additional advantage that referential names are not lexically ambiguous. It preserves a strong content relation between predicative names and referential names. This relation in content provides a principled explanation of the inferential connections between predicative and referential names, the productivity of names, and intra- and cross-linguistic uniformity. 49 Although, these resources would have to be supplemented with a syntactic and semantic system which licenses non-standard binding relations, e.g. binding without c-commanding, binding across sentences, etc. in short, a dynamic semantics.

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